Question

Could anyone please explain why the answer is 2 in 18.01 clip 1 at 40:50.
1/2(2xo)(2yo) = 2 ?

Answer 1

This is for a triangle formed by a tangent to the graph of y=1/x, the x-axis and the y-axis. At the point in the lecture you're referring to, it has been determined that the triangle will always have base 2x0 and height 2y0 for any point (x0, y0) on the curve. Using the general formula for area of a triangle we get\[A=\frac{ 1 }{ 2 }(2x_{0})(2y _{0})=2x _{0}y _{0}\]This is equal to 2 because x0 and y0 are coordinates of a point on the curve y=1/x. Multiply both sides of that equation by x and you get xy=1, so x0y0=1 and therefore 2x0y0=2.